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Bayesian multivariate sparse functional principal components analysis with application to longitudinal microbiome

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This summary is machine-generated.

We developed multivariate Sparse Functional Principal Components Analysis (mSFPCA) to model multiple microbiome temporal dynamics. This method reveals inter-relationships between complex biological trajectories.

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Area of Science:

  • Microbiome research
  • Statistical modeling
  • Functional data analysis

Background:

  • Modeling simultaneous temporal dynamics of multiple complex, nonlinear outcomes is crucial in microbiome research.
  • Existing Sparse Functional Principal Components Analysis (SFPCA) methods are limited in handling multiple trajectories and their inter-relationships.

Purpose of the Study:

  • To introduce multivariate Sparse Functional Principal Components Analysis (mSFPCA) for simultaneous characterization of multiple temporal trajectories and their inter-relationships.
  • To extend SFPCA methods for enhanced analysis of complex biological data.

Main Methods:

  • mSFPCA models each trajectory as a smooth mean plus weighted modes of variation.
  • Utilizes Cholesky decomposition for efficient covariance matrix estimation and ensures positive semi-definiteness.
  • Employs mutual information to assess temporal associations across outcome trajectories.
  • Implemented as a Bayesian algorithm using R and stan for model selection (PSIS-LOO) and validation.

Main Results:

  • mSFPCA enables simultaneous estimation of multiple trajectories, allowing correlated component scores across outcomes.
  • The method effectively characterizes temporal dynamics and inter-relationships in complex datasets.
  • Bayesian implementation facilitates robust model assessment and selection.

Conclusions:

  • mSFPCA provides a powerful, flexible tool for analyzing multivariate temporal data, particularly in microbiome research.
  • The model's general utility extends to various real-world applications requiring the analysis of multiple dynamic trajectories.